Constrained Estimation Research Articles

Constrained estimation for the binomial AR(1) model: on Bayesian approach

In this paper, we consider the constrained estimation problem for the binomial AR(1) model using Bayesian approach. We show that by using Gibbs sampling algorithm, the constrains for the parameters and latent variables can be routinely implemented. While obtaining all the full conditional distributions under the unconstrained environment, we only need to generate samples from them and make restrictions to easily described cross-sections, respectively, which avoids complex numerical integrations under the overall constraint set. In the simulation study, the performance of our algorithm is checked. Finally, the method is applied to two real data examples.

Constrained estimation of intracranial aneurysm surface deformation using 4D-CTA

Background and objectiveIntracranial aneurysms are relatively common life-threatening diseases, and assessing aneurysm rupture risk and identifying the associated risk factors is essential. Parameters such as the Oscillatory Shear Index, Pressure Loss Coefficient, and Wall Shear Stress are reliable indicators of intracranial aneurysm development and rupture risk, but aneurysm surface irregular pulsation has also received attention in aneurysm rupture risk assessment. MethodsThe present paper proposed a new approach to estimate aneurysm surface deformation. This method transforms the estimation of aneurysm surface deformation into a constrained optimization problem, which minimizes the error between the displacement estimated by the model and the sparse data point displacements from the four-dimensional CT angiography (4D-CTA) imaging data. ResultsThe effect of the number of sparse data points on the results has been discussed in both simulation and experimental results, and it shows that the proposed method can accurately estimate the surface deformation of intracranial aneurysms when using sufficient sparse data points. ConclusionsDue to a potential association between aneurysm rupture and surface irregular pulsation, the estimation of aneurysm surface deformation is needed. This paper proposed a method based on 4D-CTA imaging data, offering a novel solution for the estimation of intracranial aneurysm surface deformation.

Minimalistic estimation with stochastic constraints for closed-type tethered satellite formations

This paper aims to propose a constrained estimation scheme with minimalistic sensor settings for a class of closed-type tethered satellite formation (TSF). The estimation scheme is built on the fusion of dynamic model, priori tether length constraints, and position observation through a learning-based constrained particle filtering (CPF) design. The CPF characterizes the tether lengths as stochastic constraints and integrates these constraints within Bayesian framework based on pseudo observation and radial basis function (RBF) neural network. The RBF neural network can learn the underlying relationship between the system states and uncertain tether oscillations to establish a probability distribution function (PDF) of stochastic constraints. Nonlinear observability analysis using observability rank criterion is performed to yield insight into the minimum number of positioning sensors needed for n-body (n≥3) closed-type TSF. Furthermore, it is found that the use of pseudo observation for filtering can reduce the number of needed positioning sensors. Interestingly, the minimum number of positioning sensors required for determining all position information of n-body (n≥3) closed-type TSF is 1. Finally, the effectiveness of proposed estimation scheme is verified by posterior Cramér-Rao lower bound (PCRLB) calculation and extensive simulations. The proposed estimation scheme can be readily extended to other types of TSF. For example, the chain-type TSF.

Diffusivity-limited q-space trajectory imaging

Q-space trajectory imaging (QTI) allows non-invasive estimation of microstructural features of heterogeneous porous media via diffusion magnetic resonance imaging performed with generalised gradient waveforms. A recently proposed constrained estimation framework, called QTI+, improved QTI’s resilience to noise and data sparsity, thus increasing the reliability of the method by enforcing relevant positivity constraints. In this work we consider expanding the set of constraints to be applied during the fitting of the QTI model. We show that the additional conditions, which introduce an upper bound on the diffusivity values, further improve the retrieved parameters on a publicly available human brain dataset as well as on data acquired from healthy volunteers using a scanner-ready protocol.

A Mass-Shifting Phenomenon of Truncated Multivariate Normal Priors

We show that lower-dimensional marginal densities of dependent zero-mean normal distributions truncated to the positive orthant exhibit a mass-shifting phenomenon. Despite the truncated multivariate normal density having a mode at the origin, the marginal density assigns increasingly small mass near the origin as the dimension increases. The phenomenon accentuates with stronger correlation between the random variables. This surprising behavior has serious implications toward Bayesian constrained estimation and inference, where the prior, in addition to having a full support, is required to assign a substantial probability near the origin to capture flat parts of the true function of interest. A precise quantification of the mass-shifting phenomenon for both the prior and the posterior, characterizing the role of the dimension as well as the dependence, is provided under a variety of correlation structures. Without further modification, we show that truncated normal priors are not suitable for modeling flat regions and propose a novel alternative strategy based on shrinking the coordinates using a multiplicative scale parameter. The proposed shrinkage prior is shown to achieve optimal posterior contraction around true functions with potentially flat regions. Synthetic and real data studies demonstrate how the modification guards against the mass shifting phenomenon while retaining computational efficiency. Supplementary materials for this article are available online.

A Sharper Computational Tool for Regression

Building on previous research of Chi and Chi, this article revisits estimation in robust structured regression under the criterion. We adopt the majorization-minimization (MM) principle to design a new algorithm for updating the vector of regression coefficients. Our sharp majorization achieves faster convergence than the previous alternating proximal gradient descent algorithm by Chi and Chi. In addition, we reparameterize the model by substituting precision for scale and estimate precision via a modified Newton’s method. This simplifies and accelerates overall estimation. We also introduce distance-to-set penalties to enable constrained estimation under nonconvex constraint sets. This tactic also improves performance in coefficient estimation and structure recovery. Finally, we demonstrate the merits of our improved tactics through a rich set of simulation examples and a real data application.

State Estimation With Heading Constraints for On-Road Vehicle Tracking

In transportation networks, vehicle motions are usually subject to the constraints arising from the roads, preset sea-routes, or preset flight routes. Taking advantage of prior known information of such constraints generally produces better surveillance performance. The problem of state estimation with heading constraints, in which only the direction of the target trajectory is prior known, is considered. When only part of the trajectory information is available, the conventional constrained estimation methods cannot be used to produce constrained estimates. The heading constraints in two typical situations are investigated, one is with a straight line, the other is a circular arc. For the straight trajectory, two augmentation approaches are proposed to formulate the constraints. One, parameter augmentation, augments the base state by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$ </tex-math></inline-formula> -intercept of the constraint straight line. In the other approach, state augmentation, the states at the past time step are used to augment the base state. Two corresponding heading constraints are formulated by the augmented state’s elements and the prior known information about road direction. For a circular trajectory, the heading constraint is formulated using position and velocity components in the base state. Pseudo-measurements are constructed to incorporate the heading constraint into the estimators and result in three heading constraint Kalman filters (HCKFs). They are parameter augmentation HCKF and state augmentation HCKF in case of straight trajectory, and HCKF for circular trajectory. The discrimination of road segments at junctions is also discussed. Furthermore, the proposed constraint filters are integrated into the interacting multiple model estimator to handle on-road maneuvers with possible accelerations. Numerical simulations are conducted to evaluate the performances of the three HCKFs compared with existing methods.

Constrained finite element method for runtime modeling of soft tissue deformation

This paper presents a new constrained FEM (finite element method) for accurate and runtime modeling of soft tissue's mechanical deformation from measurement of local surface displacement. This method turns the modeling problem of tissue deformation with unknown loading input into a constrained estimation problem to online estimate physical tissue deformation. Based on linear FEM discretization, a constrained estimation algorithm is developed to optimally estimate unknown loading input and online calculate deformation from measurement of local surface displacement. Results of simulation and experimentation exhibit that the proposed method significantly promotes the FEM computational performance but still inherits the FEM advantage of physical accuracy.

Robust Filter-Based Visual Navigation Solution with Miscalibrated Bi-Monocular or Stereo Cameras

This work addressed the problem of miscalibration or decalibration of mobile stereo/bi-monocular camera setups. We especially focused on the context of autonomous vehicles. In real-world conditions, any optical system is subject to various mechanical stresses, caused by vibration, rough handling, collisions, or even thermal expansion. Such mechanical stresses change the stereo pair geometry, and as a consequence, the pre-calculated epipolar geometry or any geometric-based approach is no longer valid. The standard method, which consists of estimating the calibration online, fails in such harsh conditions. The proposed method was based on a robust linearly constrained state estimation technique able to mitigate the model mismatch without estimating the model parameters. Therefore, our solution was able to mitigate the errors with negligible use of additional computing resources. We propose to use a linearly constrained extended Kalman filter for a stereo-based visual odometry or simultaneous localization and mapping approach. Simulations confirmed that the method kept the system (and objects of the map) localized in real-time even with huge miscalibration errors and parameter variations. The results confirmed that the method was robust to a miscalibration of all the extrinsic calibration parameters even when the standard online calibration procedure failed.

Modeling and State Estimation of Linear Destination-Constrained Dynamic Systems

Goal-guided behavior and destination-directed motion appear in a wide range of human activities and physical processes. Taking advantage of such predictive information can produce better system models and state estimates. This paper focuses on modeling and filtering issues of linear dynamic systems with linear destination constraints. We examine deficiencies of the existing destination constrained (DC) estimation methods. Basically, they resort to post-treatment by imposing destination constraints on updated states only. Viewing destination constraints as an attribute implicit of the state evolution, we propose to incorporate the destination constraints accordingly, particularly on the predictive distribution of the whole state sequence. We construct a congruous DC dynamic model by sufficiently refining the relaxed dynamics with the destination constraint using the state augmentation technique, and analyze its characterization and properties. Next, for the proposed DC model, we develop an optimal DC state estimator and describe its properties. Finally, in the context of aerial surveillance, the superiority of the proposed estimator to existing DC estimators is verified by simulation results, and the effectiveness of the proposed DC dynamic model is demonstrated using real data.

Constrained estimation using penalization and MCMC

We study inference for parameters defined by either classical extremum estimators or Laplace-type estimators subject to general nonlinear constraints on the parameters. We show that running MCMC on the penalized version of the problem offers a computationally attractive alternative to solving the original constrained optimization problem. Bayesian credible intervals are asymptotically valid confidence intervals in a pointwise sense, providing exact asymptotic coverage for general functions of the parameters. We allow for nonadaptive and adaptive penalizations using the ℓp for p⩾1 penalty functions. These methods are motivated by and include as special cases model selection and shrinkage methods such as the LASSO and its Bayesian and adaptive versions. A simulation study validates the theoretical results. We also provide an empirical application on estimating the joint density of U.S. real consumption and asset returns subject to Euler equation constraints in a CRRA asset pricing model.

Constrained Nonlinear Estimation of Road Friction Coefficient and Wheel Slip for Control of Anti-Lock Braking System

Constrained Nonlinear Estimation of Road Friction Coefficient and Wheel Slip for Control of Anti-Lock Braking System

Constrained estimation in Cox model under failure-time outcome-dependent sampling design

Constrained estimation in Cox model under failure-time outcome-dependent sampling design

Trade creation and trade diversion of economic integration agreements revisited: a constrained panel pseudo-maximum likelihood approach

For PPML estimation of high-dimensional structural gravity panel models it proves useful to exploit the equilibrium restrictions imposed by the system of multilateral resistances. The main advantage of this approach lies in the functional dependence of the parameters of all dummy variables on the structural trade cost parameters. Moreover, the delta method is used to establish confidence intervals of counterfactual changes. Using the constrained panel PPML estimator for a panel of 65 countries in the period 1994–2012 indicates significant trade creation of economic integration agreements with average ranging in between 12.2 and 30.3% in 2012. Results also point to substantial domestic and international trade diversion, where the former dominates the latter.

Moving Horizon Estimation for Uncertain Networked Control Systems with Packet Loss

This paper studies a moving horizon estimation approach to solve the constrained state estimation problem for uncertain networked systems with random packet loss. The system model error range is known, and the packet loss phenomena are modeled by a binary switching random sequence. Taking the model error, the packet loss, the system constraints, and the network transmission noise into account, a time-varying weight matrix is obtained by solving a least-square problem. Then, a robust moving horizon estimator is designed to estimate the system state by minimizing an optimization problem with an arrival cost function. The proposed estimator ensures that the optimal estimated state can be obtained in the worst case. Furthermore, the asymptotic convergence of the estimator is analyzed and some sufficient conditions for convergence are given. Finally, the validity of the proposed approach can be demonstrated by numerical simulations.

Distributed Kalman Filter for Large-Scale Power Systems With State Inequality Constraints

This article is concerned with a hybrid distributed dynamic state estimation (DSE) algorithm for large-scale power grids. Based on the mixed phasor measurement unit (PMU) and remote terminal unit measurements model, a modified distributed Kalman filter (KF) is designed. Different from the centralized KF algorithm, the distributed approach is capable of independently estimating local states by local measurements. Moreover, in each local region, the multiple missing measurements problem is considered in the modified distributed KF algorithm design. The internodal transformation theory is employed to deal with the communication problem between the distributed subsystems. Therefore, the proposed method can reduce the communication latency while ensuring the estimation accuracy. Considering the inequality constraints, the particle swarm optimization algorithm and the probability-maximization method are applied to tackle the corresponding constrained estimation issue. The proposed distributed DSE algorithm is tested on an IEEE benchmark 14-bus system to demonstrate its effectiveness and applicability.

三种扰动下约束LIU估计的影响分析

三种扰动下约束LIU估计的影响分析

Linear- and Linear-Matrix-Inequality-Constrained State Estimation for Nonlinear Systems

This paper considers nonlinear state estimation subject to inequality constraints in the form of linear and linear-matrix inequalities. Rewriting the standard maximum likelihood objective function used to derive the Kalman filter allows the Kalman gain to be found by solving a constrained optimization problem with a linear objective function subject to a linear-matrix-inequality constraint. Additional constraints, such as weighted-norm- or linear-inequality constraints, that the state estimate must satisfy are easily augmented to the constrained optimization problem. The proposed constrained estimation methodology is applied in the extended Kalman filter (EKF) and sigma point Kalman filter (SPKF) frameworks. Motivated by estimation problems involving a vehicle that can rotate and translate in space, multiplicative versions of the constrained EKF and SPKF formulations are discussed. Simulation results for a ground-based mobile robot operating in a constrained three-dimensional terrain are presented and are compared to results that use the traditional multiplicative EKF and SPKF, as well as filters that enforce inequality constraints by simply projecting the state estimate into the constrained domain along the shortest Euclidean distance.

Constrained Recursive Input Estimation of Blending and Mixing Systems

Blending, mixing processes are often supported by advanced process control systems to maximise margins from available component and heat streams. Since these model-based solutions require accurate and reliable data, in weakly instrumented processes, the unknown inlet concentrations and temperatures should be estimated based on the measured outflows. This work presents a method for the reliable estimation of multiple input variables of process units. The key idea is that the input estimation problem is formulated as a constrained recursive estimation task. The applicability of the method is illustrated based on a benchmark model of a blending system. The performance of the method is compared to the moving window and Kalman Filter based solutions. The results show the superior performance of the proposed method and confirm that the apriori knowledge-based constraints improve the robustness of the estimates.

Projection‐based state estimation using noisy destination

The problem of state estimation with a destination constraint using the noisy prior information of the destination is investigated. With the utilisation of constraint information in estimation system, the estimation accuracy can be significantly enhanced. A projection-based constrained state estimation method is proposed to address this problem. In this method, the unscented Kalman filter is employed to obtain the unconstrained estimation. The Taylor series expansion is adopted to deal with the non-linearity of the destination constraint and the projection method is used to project the unconstraint estimate onto the constraint surface. Monte Carlo simulation results are presented to illustrate the effectiveness of the new approach.